Question 684828
Start with 3x + 2y = 7
solve for y, subtract 3x  from both sides
2y = -3x + 7
y = {{{(-3/2)x + 7/2}}}
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slope is {{{(-3/2)}}}
Parallel lines have the same slope.
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Using slope and the point,
y - -3 = {{{(-3/2)}}}(x-8)
y + 3 = {{{(-3/2)x + 8(3/2)}}}
y +3 = {{{(-3/2)x + 24/2}}}
y = {{{(-3/2)x + 12 - 3 }}}
{{{highlight_green(y=(-3/2)x + 9)}}}
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First error was in solving for y, when you subtract the 3x the 2y remains positive.
Second error was in subtracting fractions {{{-24/2 - 3 <>-21/2}}}
if you were on the right track, {{{-24/2 - 3(2/2) = -24/2 - 6/2 = -30/2 = -15}}} 
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